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Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
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SYSNO ASEP 0575046 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle Author(s) Krejčiřík, D. (CZ)
Lotoreichik, Vladimir (UJF-V) ORCID, SAI
Vu, T. (CZ)Number of authors 3 Article number 63 Source Title Applied Mathematics and Optimization. - : Springer - ISSN 0095-4616
Roč. 88, č. 2 (2023)Number of pages 33 s. Publication form Print - P Language eng - English Country US - United States Keywords Robin Laplacian ; Lowest eigenvalue ; Spectral optimisation ; Triangles OECD category Applied mathematics R&D Projects GA21-07129S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UJF-V - RVO:61389005 UT WOS 001049245900003 EID SCOPUS 85168304684 DOI 10.1007/s00245-023-10033-1 Annotation We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2024 Electronic address https://doi.org/10.1007/s00245-023-10033-1
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